----- Original Message ---- From: Fred lunnon <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, January 11, 2008 12:54:07 PM Subject: Re: [math-fun] Moebius madness on Youtube Nicely done. And it grieves me to have to admit that, although I've been concerned with these groups for a good few years, I had no idea that the isomorphism of the Moebius group in n-space with the Euclidean group in (n+1)-space had such a straightforward demonstration! WFL On 1/11/08, Henry Baker <hbaker1@pipeline.com> wrote:
Very cool animation of Moebius transformations:
And, it is also isomorphic to Lorentz group in (n+2)-space, i.e. SO(n+1,1). To demo this isomorphism, just fly through space at relativistic velocities. A Lorentz transformation of your spacecraft induces a mapping of the celestial sphere which is a Moebius transformation. Gene ____________________________________________________________________________________ Looking for last minute shopping deals? Find them fast with Yahoo! Search. http://tools.search.yahoo.com/newsearch/category.php?category=shopping